Diameter and radius in the Manhattan metric
type: Item
instance of: scholarly article
title: Diameter and radius in the Manhattan metric
zbMATH Open document ID: 0696.52007
DOI: 10.1007/BF02187795
author: Du Ding-Zhu
author: Daniel J. Kleitman
published in: Discrete \& Computational Geometry
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131122
review text: A maximum d set inside given rectilinearly bounded set \(R\subset Z^ n\) of lattice points is by definition a set which has \(L^ 1\)-diameter d and the largest number of points possible. A general question, suggested by Erdős, is for what d and general-sized regions R there is a maximum d set which is contained in a ball of radius d/2 and center in R. The second author and Fellows, who found a partial answer to the Erdős question above, conjectured that the answer is always positive if the center of the ball is not required to be a lattice point. The authors provide in the paper under review a partial verification of this conjecture. As an example, they show that if \(d_ j\) is the largest coordinate difference in the \(j^{th}\) component among members of R and if e(R) is the number of even integers among \(d_ j\) then the conjecture is completely resolved.
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 4140701
zbMATH Keywords: maximum d set
reviewed by: Rade Živaljević
MaRDI profile type: Publication
cites work: On a combinatorial conjecture of Erdös
cites work: Radius and diameter in Manhattan lattices
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description: scientific article; zbMATH DE number 4140701